Electroencephalograph (EEG) and Holter EEG data compression techniques which allow perfect reconstruction of the recorded waveform from the compressed one are presented and discussed. Data compression permits one to achieve significant reduction in the space required to store signals and in transmission time. The Huffman coding technique in conjunction with derivative computation reaches high compression ratios (on average 49% on Holter and 58% on EEG signals) with low computational complexity. By exploiting this result a simple and fast encoder/decoder scheme capable of real-time performance on a PC was implemented. This simple technique is compared with other predictive transformations, vector quantization, discrete cosine transform (DCT), and repetition count compression methods. Finally, it is shown that the adoption of a collapsed Huffman tree for the encoding/decoding operations allows one to choose the maximum codeword length without significantly affecting the compression ratio. Therefore, low cost commercial microcontrollers and storage devices can be effectively used to store long Holter EEG's in a compressed format.